14. starptautiskā konference 2012 - Latvijas Jūras akadēmija

Proceedings of 14th International conference „Maritime Transport and Infrastructure - 2012” y a y a y a y 0(27)1 2 3The coefficients of equation are constant therefore it is possible to use characteristic equationfor solving equation.3 2 a a a 0 . (28)1The parameters of the device are chosen in order to ensure that one rot of equation is real butrest two are complex joint and all 3 rots has negative real parts:231 m; 2, 3 h qj . (29)In such situation the equation (27) describes the process of ceased oscillations. In order toensure that the real parts of equation (28) are negative in accordance with theorem of Gurvic [5], it isnecessary that equations are accomplished sufficiently:The general solution of equation (28) is stated with formula:a11a1 0; 0.(30)a a32mthty C1e e C2cos qt C3sin qt , (31)Where C1, C2,C3are undetermined constants of integration orwhereA2 23 C2 C3; tg .C2mthty C1 e Ae cos qt , (32)CThe particular solutions of (26) of non – homogenous equation (26) is acquired with methodof non- defined coefficients:y fa 3. (33)Using solutions (32) and (33) a general solution must be written (2):mthtfy C1e Ae cosqt , (34)aWhich describes process of ceased oscillations if m>0 and h>0.383